JOURNAL BROWSE
Search
Advanced SearchSearch Tips
AN IDEAL-BASED ZERO-DIVISOR GRAPH OF 2-PRIMAL NEAR-RINGS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
AN IDEAL-BASED ZERO-DIVISOR GRAPH OF 2-PRIMAL NEAR-RINGS
Dheena, Patchirajulu; Elavarasan, Balasubramanian;
  PDF(new window)
 Abstract
In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact -subspace. We also study the zero-divisor graph (R) with respect to the completely semiprime ideal I of N. We show that (R), where is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph (R).
 Keywords
graph;prime ideal;2-primal;Zariski topology and cycle;
 Language
English
 Cited by
1.
Poset Properties Determined by the Ideal - Based Zero-divisor Graph,;;

Kyungpook mathematical journal, 2014. vol.54. 2, pp.197-201 crossref(new window)
1.
Poset Properties Determined by the Ideal - Based Zero-divisor Graph, Kyungpook mathematical journal, 2014, 54, 2, 197  crossref(new windwow)
 References
1.
D. D. Anderson and M. Naseer, Beck's coloring of a commutative ring, J. Algebra 159 (1993), no. 2, 500-514 crossref(new window)

2.
D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), no. 2, 434-447 crossref(new window)

3.
I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208-226 crossref(new window)

4.
J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976

5.
P. Dheena and B. Elavarasan, On strong IFP near-ring, Submitted

6.
R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989

7.
J. R. Munkres, Topology, Prentice-Hall of Indin, New Delhi, 2005

8.
G. Pilz, Near-Rings, North-Holland, Amsterdam, 1983

9.
S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra 31 (2003), no. 9, 4425-4443 crossref(new window)

10.
K. Samei, On summand ideals in commutative reduced rings, Comm. Algebra 32 (2004), no. 3, 1061-1068 crossref(new window)

11.
K. Samei, The zero-divisor graph of a reduced ring, J. Pure Appl. Algebra 209 (2007), no. 3, 813-821 crossref(new window)

12.
S. H. Sun, Noncommutative rings in which every prime ideal is contained in a unique maximal ideal, J. Pure Appl. Algebra 76 (1991), no. 2, 179-192 crossref(new window)